1) This is a seminar for topology/geometry and Arithmetics (number theory).

2) Aim: One of the aims of the working group is to understand the

theorem that states the existence of an injection from the absolute

Galois group Gal(\bar(Q)/Q) into the profinite version of the

Grothendieck -Teichmuller group.

Organization: The first three sessions of the working group, concern an

introduction to the paper of Y. Ihara « Automorphisms of Pure Sphere

Braid groups and Galois representations » (The Grothendieck Festschrift

vol II). The idea of this seminar is that one topologist and one

arithmetician explains their point of view, on (a part of) this paper.

For this week we will start with basic tools.

The speakers will be Danica Kosanovic (topology) and Gaultier Ponsinet

(number theory).

For the next week Gaultier Ponsinet will give the part 2 of his talk.

(2nd person tbc).

Gaultier will in particular focus on the following points:

« The goal is to explain (1.4.1), (1.4.2) and (1.4.3) of Ihara's

article. To do so, we will recall the definition and some properties of

the absolute Galois group of a field, of the fundamental group of a

topological space, and finally, of the étale fundamental group of scheme

which links the two previous objects. The book of T. Szamuely « Galois

groups and fundamental groups » and « The algebraic fundamental group »

of F. Oort are good references. »

© MPI f. Mathematik, Bonn | Impressum & Datenschutz |